Oikonomou Thomas, Bagci G Baris
Department of Physics, School of Science and Technology, Nazarbayev University, 53 Kabanbay Batyr Avenue, Astana 010000, Kazakhstan.
Department of Materials Science and Nanotechnology Engineering, TOBB University of Economics and Technology, 06560 Ankara, Turkey.
Phys Rev E. 2017 Nov;96(5-2):056101. doi: 10.1103/PhysRevE.96.056101. Epub 2017 Nov 20.
Plastino et al. [Plastino et al., Phys. Rev. E 94, 012145 (2016)1539-375510.1103/PhysRevE.94.012145] recently stated that the Rényi entropy is not suitable for thermodynamics by using functional calculus, since it leads to anomalous results unlike the Tsallis entropy. We first show that the Tsallis entropy also leads to such anomalous behaviors if one adopts the same functional calculus approach. Second, we note that one of the Lagrange multipliers is set in an ad hoc manner in the functional calculus approach of Plastino et al. Finally, the explanation for these anomalous behaviors is provided by observing that the generalized distributions obtained by Plastino et al. do not yield the ordinary canonical partition function in the appropriate limit and therefore cannot be considered as genuine generalized distributions.
普拉斯蒂诺等人[普拉斯蒂诺等人,《物理评论E》94,012145(2016)1539 - 3755 10.1103/PhysRevE.94.012145]最近指出,通过泛函演算,雷尼熵不适用于热力学,因为与Tsallis熵不同,它会导致异常结果。我们首先表明,如果采用相同的泛函演算方法,Tsallis熵也会导致这种异常行为。其次,我们注意到在普拉斯蒂诺等人的泛函演算方法中,拉格朗日乘数之一是以特设方式设定的。最后,通过观察普拉斯蒂诺等人得到的广义分布在适当极限下不会产生普通的正则配分函数,因此不能被视为真正的广义分布,从而对这些异常行为给出了解释。